Difference between revisions of "Manuals/calci/IMSQRT"
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<math>\sqrt{z}=\sqrt{x+iy}=\sqrt{r.e^{i\theta}}=\sqrt{{r}(cos(\frac{θ}{2})+isin(\frac{θ}{2})}</math> | <math>\sqrt{z}=\sqrt{x+iy}=\sqrt{r.e^{i\theta}}=\sqrt{{r}(cos(\frac{θ}{2})+isin(\frac{θ}{2})}</math> | ||
*where <math>r</math> is the modulus of <math>z</math>. <math>r=\sqrt{x^2+y^2}</math> | *where <math>r</math> is the modulus of <math>z</math>. <math>r=\sqrt{x^2+y^2}</math> | ||
| − | *And <math>\theta</math> is the argument of <math>z</math>. <math> θ=tan^{-1}(y/x)</math> also <math>θ∈(-pi | + | *And <math>\theta</math> is the argument of <math>z</math>. <math> θ=tan^{-1}(y/x)</math> also <math>θ∈(-\pi,\pi]</math>. |
*We can use COMPLEX function to convert real and imaginary number in to a complex number. | *We can use COMPLEX function to convert real and imaginary number in to a complex number. | ||
Revision as of 22:43, 25 December 2013
IMSQRT(z)
- is the complex number is of the form
is the complex number is of the form 
Description
- This function gives square root of a complex number.
- IMSQRT(z), where z is the complex number is in the form of "x+iy".
- where x&y are the real numbers. imaginary unit ..
- The square root of a complex number is defined by:
imaginary unit .
.Failed to parse (syntax error): {\displaystyle \sqrt{z}=\sqrt{x+iy}=\sqrt{r.e^{i\theta}}=\sqrt{{r}(cos(\frac{θ}{2})+isin(\frac{θ}{2})}}
- where is the modulus of .
- And is the argument of . Failed to parse (syntax error): {\displaystyle θ=tan^{-1}(y/x)} also Failed to parse (syntax error): {\displaystyle θ∈(-\pi,\pi]} .
- We can use COMPLEX function to convert real and imaginary number in to a complex number.
is the modulus of 
is the argument of Examples
- =IMSQRT("2+3i")=1.67414922803554+0.895977476129838i
- =IMSQRT("-4-5i")=1.09615788950152-2.2806933416653i
- =IMSQRT("7")=2.64575131106459
- =IMSQRT("8i")=2+2i
See Also